Particle accelerators, such as the Large Hadron Collider, use magnetic fields to steer charged particles around a ring. Consider a proton ring with 36 identical bending magnets connected by straight segments. The protons move along a -m-long circular arc as they pass through each magnet. What magnetic field strength is needed in each magnet to steer protons around the ring with a speed of ? Assume that the field is uniform inside the magnet, zero outside.
The strength of magnetic field needed
The particle accelerator motion is specified as a particles travelling in a uniform circular motion perpendicular to the magnetism at a constant speed. The radius of the circular motion induced by the magnetization is connected to the motion's radius.
Where q is the particle's charged, v is the particle's speed, B is the magnetic field, and m is the particle's mass. Since a magnet has such a length of, the length of a circular pattern composed of 36 magnets will be, which matches the circumference of such path. As a basis, we use it to compute the motion's radius.
The challenge is to find the needed magnetic field.
Although the evidence is weak, there has been concern in re-cent years over possible health effects from the magnetic fields generated by electric transmission lines. A typical high-voltage transmission line is above the ground and carries a current at a potential of.
a. What is the magnetic field strength on the ground directly under such a transmission line?
b. What percentage is this of the earth’s magnetic field of?
The earth’s magnetic dipole moment is .
a. What is the magnetic field strength on the surface of the earth at the earth’s north magnetic pole? How does this compare to the value in Table 29.1? You can assume that the current loop is deep inside the earth.
b. Astronauts discover an earth-size planet without a magnetic field. To create a magnetic field at the north pole with the same strength as earth’s, they propose running a current through a wire around the equator. What size current would be needed?
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